In one design, such machines conventionally can comprise a base structure providing a guideway for horizontal movement of a column which extends vertically from the base structure. The column provides a support for a vertically movable carriage which in turn locates a horizontally movable quill on which a measuring probe is mounted. Such a machine provides for three co-ordinate measurement or checking of a workpiece. The carriage movement is effected by an electric motor arrangement driving a rigidly connected carriage and counterbalance structure, the counterbalance being required to compensate for the combined weight of the carriage and the motor arrangement.